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Popular >

(cos(x))/(cos(x))=(cos(x))/(1+sin(x))

Solución

\frac{cos ( x )}{cos ( x )} = \frac{cos ( x )}{1 + sin ( x )}

Solución

x = 2 πn + 2 π

+1

Pasos de solución

\frac{cos ( x )}{cos ( x )} = \frac{cos ( x )}{1 + sin ( x )}

Restar

\frac{cos ( x )}{1 + sin ( x )}

de ambos lados

1 - \frac{cos ( x )}{1 + sin ( x )} = 0

Simplificar

1 - \frac{cos ( x )}{1 + sin ( x )} : \frac{1 + sin ( x ) - cos ( x )}{1 + sin ( x )}

\frac{1 + sin ( x ) - cos ( x )}{1 + sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

1 + sin (x) - cos (x) = 0

Re-escribir usando identidades trigonométricas

1 + 2 sin (x - \frac{π}{4}) = 0

Mover

1

al lado derecho

2 sin (x - \frac{π}{4}) = - 1

Dividir ambos lados entre

2

sin (x - \frac{π}{4}) = - \frac{2}{2}

Soluciones generales para

sin (x - \frac{π}{4}) = - \frac{2}{2}

x - \frac{π}{4} = \frac{5 π}{4} + 2 πn, x - \frac{π}{4} = \frac{7 π}{4} + 2 πn

Resolver

x - \frac{π}{4} = \frac{5 π}{4} + 2 πn : x = 2 πn + \frac{3 π}{2}

Resolver

x - \frac{π}{4} = \frac{7 π}{4} + 2 πn : x = 2 πn + 2 π

x = 2 πn + \frac{3 π}{2}, x = 2 πn + 2 π

Siendo que la ecuación esta indefinida para:

2 πn + \frac{3 π}{2}

x = 2 πn + 2 π

Ejemplos populares

-2cos(θ)-sqrt(3)=0

- 2 cos (θ) - 3 = 0

4 cos^{2} (2 x) = 1

sec (x) = - 4.5973

2cos(9x)=2-2cos(9x)

2 cos (9 x) = 2 - 2 cos (9 x)

sin(2x)=3sqrt(2),-pi<= x<= pi

sin (2 x) = 32, - π \leq x \leq π